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?aknys
Neneigiamasis skai?ius b ¡Ý 0, kuriam yra
teisinga lygyb? b n = a , vadinamas
aritmetine n -ojo laipsnio ?aknimi i? a .
a ¡Ý 0, o n ¡Ý 2 ¨C lyginis nat¨±ralusis
skai?ius.
?ymime

b = a;
n

a ¨C n -ojo laipsnio ?aknies po?aknis,
b ¨C n -ojo laipsnio ?aknies reik?m?.
Pvz.:

16 = 4, (n = 2), nes 4 2 = 16 ir 4 > 0;
4
6

81 = 3, (n = 4), nes 34 = 81 ir 3 > 0;

64 = 2, (n = 6), nes 26 = 64 ir 2 > 0.

Lyginio laipsnio ?aknis su neigiamuoju
po?akniu neturi prasm?s.
Pvz.:
4

- 16 , ? 3
Sakykime a ¨C bet koks realusis skai?ius,

n ¡Ý 3 ¨C nelyginis nat¨±ralusis skai?ius.
Skai?ius b (jo ?enklas sutampa su a
?enklu), kuriam yra teisinga lygyb? b n =
a , vadinamas n -ojo laipsnio ?aknimi i?
a.
Pvz.:
3
3
5

8 = 2, (n = 3), nes 23 = 8;

? 8 = ?2, (n = 3), nes (?2) = ?8;
3

32 = 2, (n = 5), nes 25 = 32;
Kai ?aknies laipsnio rodiklis nelyginis, yra
teisinga lygyb?

n
Pvz.:

3
5

? a = ?n a

? 2 = ?3 2 ;

? 32 = ? 32 = ?2.
5
n-ojo laipsnio ?aknys i? neigiam?j? skai?i?:
n

a =a
n

Pvz.:

n

kai n ¨C lyginis.

(?5) = ? 5 = 5;
2

a =a
n

3

4

(?5) = ? 5 = 5;
4

kai n ¨C nelyginis.

(?5) = ?5;
3

5

(?5) = ?5;
5
?akn? savyb?s

n

Pvz. :

3

a ? b = a ?b
n

n

2 ? 3 500 = 3 2 ? 500 = 3 1000 = 3 103 = 10
n

Pvz. :

4

n

a n a
a: b= n =
b
b
n

3 4 3 3 4 3 16 4
3:4
=
:
=
? = 16 = 4 2 4 = 2
16
1 16
1 3
( a)
n

Pvz. :

k

( 4)

= a
n

3

k

= 4 = 64 = 8
3
a =

n k

Pvz. :

3 4
3

2=

n?k

3?4

a

2= 2
12

7 = 2?3 7 = 6 7
n?k

Pvz. :

6
8

a = a
k

n

3

5 =

2?3

5 = 5

16 =

2?4

2 = 2

3

4
a b = a ?b
n

n

Pvz. :

n

4 3 = 4 ? 3 = 16 ? 3 = 48
2

2 5 = 2 ? 5 = 8 ? 5 = 40
3

3

3
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Ad

?Aknys

  • 2. Neneigiamasis skai?ius b ¡Ý 0, kuriam yra teisinga lygyb? b n = a , vadinamas aritmetine n -ojo laipsnio ?aknimi i? a . a ¡Ý 0, o n ¡Ý 2 ¨C lyginis nat¨±ralusis skai?ius. ?ymime b = a; n a ¨C n -ojo laipsnio ?aknies po?aknis, b ¨C n -ojo laipsnio ?aknies reik?m?.
  • 3. Pvz.: 16 = 4, (n = 2), nes 4 2 = 16 ir 4 > 0; 4 6 81 = 3, (n = 4), nes 34 = 81 ir 3 > 0; 64 = 2, (n = 6), nes 26 = 64 ir 2 > 0. Lyginio laipsnio ?aknis su neigiamuoju po?akniu neturi prasm?s. Pvz.: 4 - 16 , ? 3
  • 4. Sakykime a ¨C bet koks realusis skai?ius, n ¡Ý 3 ¨C nelyginis nat¨±ralusis skai?ius. Skai?ius b (jo ?enklas sutampa su a ?enklu), kuriam yra teisinga lygyb? b n = a , vadinamas n -ojo laipsnio ?aknimi i? a. Pvz.: 3 3 5 8 = 2, (n = 3), nes 23 = 8; ? 8 = ?2, (n = 3), nes (?2) = ?8; 3 32 = 2, (n = 5), nes 25 = 32;
  • 5. Kai ?aknies laipsnio rodiklis nelyginis, yra teisinga lygyb? n Pvz.: 3 5 ? a = ?n a ? 2 = ?3 2 ; ? 32 = ? 32 = ?2. 5
  • 6. n-ojo laipsnio ?aknys i? neigiam?j? skai?i?: n a =a n Pvz.: n kai n ¨C lyginis. (?5) = ? 5 = 5; 2 a =a n 3 4 (?5) = ? 5 = 5; 4 kai n ¨C nelyginis. (?5) = ?5; 3 5 (?5) = ?5; 5
  • 7. ?akn? savyb?s n Pvz. : 3 a ? b = a ?b n n 2 ? 3 500 = 3 2 ? 500 = 3 1000 = 3 103 = 10
  • 8. n Pvz. : 4 n a n a a: b= n = b b n 3 4 3 3 4 3 16 4 3:4 = : = ? = 16 = 4 2 4 = 2 16 1 16 1 3
  • 9. ( a) n Pvz. : k ( 4) = a n 3 k = 4 = 64 = 8 3
  • 10. a = n k Pvz. : 3 4 3 2= n?k 3?4 a 2= 2 12 7 = 2?3 7 = 6 7
  • 11. n?k Pvz. : 6 8 a = a k n 3 5 = 2?3 5 = 5 16 = 2?4 2 = 2 3 4
  • 12. a b = a ?b n n Pvz. : n 4 3 = 4 ? 3 = 16 ? 3 = 48 2 2 5 = 2 ? 5 = 8 ? 5 = 40 3 3 3